Question

Water has a mass per mole of 18.0 g/mol, and each water molecule (h2o) has 10 electrons. (a) how many electrons are there in 7.74 liters of water? (1 liter is equivalent to 1.00 × 10-3 m3) (b) what is the net charge of all these electrons?

Answer 1

The number of electrons in 7.74 liters of water is calculated by first determining the mass of water, converting that mass to moles, and then multiplying by the number of electrons per water molecule. This gives a total of 2.58 × 10·¶ electrons. The net charge of all these electrons is -2.58 × 10·¶ elementary charges, but the water itself remains electrically neutral.

Step-by-step explanation:

Calculating the Number of Electrons in Water

To determine the number of electrons in 7.74 liters of water, we first need to calculate the number of moles of water present in that volume. The density of water is 1 g/mL, so 1 liter of water has a mass of 1000 g. Using the molar mass of water, which is 18 g/mol, we can convert this mass to moles.

7.74 liters × 1000 g/liter = 7740 g of water

To convert grams to moles, we use the molar mass as a conversion factor:

7740 g × (1 mol/18 g) = 430 moles of water

Since each water molecule has 10 electrons, we can calculate the total number of electrons:

430 moles × 6.02 × 10²³ molecules/mol × 10 electrons/molecule = 2.58 × 10·¶ electrons

Regarding part (b) of the question, the net charge of all these electrons, electrons carry a charge of -1 elementary charge each, therefore:

Total net charge = 2.58 × 10·¶ electrons × -1 elementary charge/electron = -2.58 × 10·¶ elementary charges

However, it is important to note that these electrons are part of water molecules, and thus the overall charge of the 7.74 liters of water is neutral, as the protons in the hydrogen atoms balance out the charge of the electrons.

Answer 2

Answer: a)
`2.58* 10^(27)` electrons are present is 7.74 L of water.

b)
`2.7* 10^(8) Coulombs` is the net charge of all these electrons

Step-by-step explanation:

a) Molar mass of the water = 18 g/mol

Volume of water = 7.74 L

Density of water = 1000 g/L

Mass of water in 7.74 L of water :

`density=1000 g/L=(mass)/(volume)=(mass)/(7.74 L)`

Mass of the water = 7740 g

Moles of water =
`\frac{\text{mass of water}}{\text{molar mass of water}}=(7740 g)/(18 g/mol)=430 moles`

`1 mol=6.022* 10^(23)`molecules

Number of water molecules in 430 moles:

`430* 6.022* 10^(23) =2.58* 10^(26)`molecules

1 molecule water contains = 10 electrons

Then
`2.58* 10^(26) molecules=2.58* 10^(26)* 10=2.58* 10^(27)` electrons

`2.58* 10^(27)` electrons are present is 7.74 L of water.

b) The net charge of all these
`2.58* 10^(27)` electrons:

Charge on 1 electron =
`-1.602* 10^(-19) Coulombs`

The net charge of all these
`2.58* 10^(27)` electrons:

`2.58* 10^(27)* 1.602* 10^(-19) C=2.7* 10^(8) Coulombs`

`2.7* 10^(8) Coulombs` is the net charge of all these electrons